In this paper, the Ostrowski inequality for $s$-convex functions in the third sense is studied. By applying Hölder and power mean integral inequalities, the Ostrowski inequality is obtained for the functions, the absolute values of the powers of whose derivatives are $s$-convex in the third sense. In addition, by means of these inequalities, an error estimate for a quadrature formula via Riemann sums and some relations involving means are given as applications.